docs: def mnl_estimate(data, chosen, numalts, GPU=False, coeffrange=(-3, 3),
                   weights=None, lcgrad=False, beta=None):
      """
      Calculate coefficients of the MNL model.
  
      Parameters
      ----------
      data : 2D array
          The data are expected to be in "long" form where each row is for
          one alternative. Alternatives are in groups of `numalts` rows per
          choosers. Alternatives must be in the same order for each chooser.
      chosen : 2D array
          This boolean array has a row for each chooser and a column for each
          alternative. The column ordering for alternatives is expected to be
          the same as their row ordering in the `data` array.
          A one (True) indicates which alternative each chooser has chosen.
      numalts : int
          The number of alternatives.
      GPU : bool, optional
      coeffrange : tuple of floats, optional
          Limits of (min, max) to which coefficients are clipped.
      weights : ndarray, optional
      lcgrad : bool, optional
      beta : 1D array, optional
          Any initial guess for the coefficients.
  
      Returns
      -------
      log_likelihood : dict
          Dictionary of log-likelihood values describing the quality of
          the model fit.
      fit_parameters : pandas.DataFrame
          Table of fit parameters with columns 'Coefficient', 'Std. Error',
          'T-Score'. Each row corresponds to a column in `data` and are given
          in the same order as in `data`.
  
      See Also
      --------
      scipy.optimize.fmin_l_bfgs_b : The optimization routine used.
  
      """
      logger.debug(
          'start: MNL fit with len(data)={} and numalts={}'.format(
              len(data), numalts))
      atype = 'numpy' if not GPU else 'cuda'
  
      numvars = data.shape[1]
      numobs = data.shape[0] // numalts
  
      if chosen is None:
          chosen = np.ones((numobs, numalts))  # used for latent classes
  
      data = np.transpose(data)
      chosen = np.transpose(chosen)
  
      data, chosen = PMAT(data, atype), PMAT(chosen, atype)
      if weights is not None:
          weights = PMAT(np.transpose(weights), atype)
  
      if beta is None:
          beta = np.zeros(numvars)
      bounds = [coeffrange] * numvars
  
      with log_start_finish('scipy optimization for MNL fit', logger):
          args = (data, chosen, numalts, weights, lcgrad)
          bfgs_result = scipy.optimize.fmin_l_bfgs_b(mnl_loglik,
                                                     beta,
                                                     args=args,
                                                     fprime=None,
                                                     factr=10,
                                                     approx_grad=False,
                                                     bounds=bounds
                                                     )
  
      if bfgs_result[2]['warnflag'] > 0:
          logger.warn("mnl did not converge correctly: %s",  bfgs_result)
  
      beta = bfgs_result[0]
      stderr = mnl_loglik(
          beta, data, chosen, numalts, weights, stderr=1, lcgrad=lcgrad)
  
      l0beta = np.zeros(numvars)
      l0 = -1 * mnl_loglik(l0beta, *args)[0]
      l1 = -1 * mnl_loglik(beta, *args)[0]
  
      log_likelihood = {
          'null': float(l0[0][0]),
          'convergence': float(l1[0][0]),
          'ratio': float((1 - (l1 / l0))[0][0])
      }
  
      fit_parameters = pd.DataFrame({
          'Coefficient': beta,
          'Std. Error': stderr,
          'T-Score': beta / stderr})
  
      logger.debug('finish: MNL fit')
      return log_likelihood, fit_parameters